We give an O(n log n) algorithm for computing the girth (shortest cycle) of an undirected n-vertex planar graph. Our solution extends to any graph of bounded genus. This improves u...
We proved that every planar triangle-free graph with n vertices has a subset of vertices that induces a forest of size at least (71n + 72)/128. This improves the earlier work of S...
Wang and Lih conjectured that for every g 5, there exists a number M(g) such that the square of a planar graph G of girth at least g and maximum degree M(g) is (+1)-colorable. ...
Jeager et al introduced a concept of group connectivity as an generalization of nowhere zero flows and its dual concept group coloring, and conjectured that every 5-edge connected...